Adobe doesn't offer the option to use SFTP with private key authentication with Dreamweaver.
According to Adobes web site you can use FTPS where there is a certificate used for authenticating that your connecting to the correct server and obviously encryption, but nothing about the use of SFTP with private key authentication.
You can read all about what is available with Dreamweaver remote server connect function here: http://helpx.adobe.com/dreamweaver/using/connect-remote-server.html
You can use Putty's Pageant and FileZilla which I know is a bummer considering the cost of Adobe Dreamweaver (I have it) but appears to be the only other secure option.
You can read about how to use the 2 here: http://wiki.filezilla-project.org/Howto